Description: The Principle of Finite
Induction (mathematical induction). Corollary
7.31 of [TakeutiZaring] p. 43.
The simpler hypothesis shown here was
suggested in an email from "Colin" on 1-Oct-2001. The
hypothesis states
that is a set
of natural numbers, zero belongs to , and
given any member of the member's successor also belongs to
. The
conclusion is that every natural number is in .
(Contributed by NM, 22-Feb-2004.) (Proof shortened by Andrew Salmon,
27-Aug-2011.)